How much force do the students need to exert (combined) if they want to give the car a forward acceleration of 0.5 m/s2

Question

Two students are pushing a stalled car down the street. The car has a mass of 1500 kg and experiences a friction force between the tires and the road of 350 N. How much force do the students need to exert (combined) if they want to give the car a forward acceleration of 0.5 m/s²?

Answer 1

The solution comes Newton's Second Law: ΣF = ma, where ΣF is going to be the SUM of all forces acting on the car, m is the mass of the car and a will be acceleration that the car undergoes due to those forces.

Now we only need to be concerned with the horizontal motion of the car, so we only need to consider the horizontal components of the equation.

Let F_A be the combined force applied horizontally by the two students and let f_friction be the frictional force that the surface exerts on the cars tires. so ΣF will be equal to

ΣF = F_A -f_friction (the friction will be opposing the motion of the car)

Now

ΣF = ma

F_A -f_friction =ma and given the mass of the car, the desired acceleration and the frictional force we have

F_A = f_friction +ma = (350 N) + (1500 kg)(0.5 m/s²) = 350 N + 750 N = 1100 N

So the students would have to exert a total (and horizontal) applied force of 1100 N to accelerate the car at 0.5 m/s².